Just because you see it in print does not mean it is correct. Peonies do not have rhizomes or rhizomatous growth.

A popular magazine is not always the best choice for horticultural information. Instead, research horticulture or science based websites.

Try the American Peony Society for plant specific info. Not once do they mention bulbs, tubers or rhizomes :-)

And this fact sheet from the UA extension service will explain all you need to know about rhizomes: Rhizomes